First of all, if you're trying to link Bana and Norton together, then you've already failed. Two different franchises,
No they were not. If you watch the second film its very much a continuation of the first, with the opening credits being him trying to rid himself of the powers.
The Punisher was a total reboot, the second Hulk film was a sequel.
Actually, the Incredible Hulk pulled the same stunt Punisher: War Zone did by giving the main character a different origin but doing so in flashbacks and/or dialogue rather than fully exploring them.
Nope, they didnt. Nowhere in the film does it mention his origin.
As I said, the flashbacks (that resembled the old tv series origin) seemed to indicate the attempted removal of the powers rather than the recieving of them.